How to Build Number Sense thru Staircases
Knowing how to build number sense is vital for developing deep mathematical awareness. Cuisenaire Rods are the most vital tools to building number sense, and today we are going to look at Staircase activities that provide one way to build number sense through Cuisenaire Rods.
Developing a child's mathematical awareness is key to achieving that "aaah, ha" moment and according to Gattegno it is the only thing one can really "educate." One of the basic Cuisenaire rod activities that Gattegno emphasizes is staircase work. It seems like such a simple activity that one cannot imagine there is much that can be gained from it.
In fact, there is a lot to be gained from it. Number sense in its most basic definition is the fluid understanding of the innumerable relationships that exist between numbers. Staircase work begins to develop this awareness of how each number compares and relates to each other.
Discovering the Staircase
Four is less than five. Six is less than ten. Eight is more than seven. The child can certainly discover staircases on their own by merely having free time to build and play with Cuisenaire rods. You can also lead the child to the discovery of a complete staircase through task based instructions like this:
- Find one rod of every color.
- Show me the shortest rod.
- Show me the tallest rod.
- How would you organize the rods from shortest to tallest?
Such an example would most likely lead a child to determine for themselves the order of shortest to tallest or vice versa. Of course, if they don't right away determine this for themselves, give them time to naturally discover the staircase. Of course, if one were in a hurry for this discover to happen, you could model the staircase and ask the child their thoughts on your creation. They might be interested in giving it a go themselves. However, this is just not as fun as letting them discover it for themselves.
As they build staircases, the child begins to see how these rods illustrate relationships. Purple is shorter than yellow. Dark green is shorter than orange. Tan is taller than black and so on.
Staircase work can also offer opportunity to discover more specific relationships like red is one white rod taller than white rod, and light green is one white taller than red, and that this relationship continues with each taller rod.
There is opportunity to discover complements as well. When you build a full staircase, you would find all the rods that would extend each stair to the height of the tallest stair (the orange rod). In doing such an activity, the student is exploring all the ways to build ten using just two rods (complements).
You can continue exploring complements of the other rods by shortening the staircase by one rod. The student's fluid understanding of number sense continues to develop as they make smaller and smaller staircases and the corresponding complements.
Odd and Even Discovery
We can also use staircase work to discover the concept of odd and even. This can be done several ways.
- Which rods can be made of pairs of the same color rod?
- Which rods need an additional white rod to complete the staircase?
- Which rods can be made with all red rods?
You can expand upon odd and even by building staircases of just even rods and then just odd rods. You can see how even numbers relate to just even numbers and the same with odd numbers. You can also compare the odd staircase to the even staircase.
Bringing the student back to staircase work sounds like a task that could get old quickly, and so it is important to vary the task. Providing templates allow the student freedom of expression in building staircases. The student can explore filling the staircase with as many light green rods as they desire or with an assorted rod sizes of their choosing. Other constraints include:
- Use only white, red and green to build your staircase.
- Use only odd numbers rods to build your staircase.
- Create a staircase with only white, purple and yellow rods.
Once children discover staircases for themselves, they will fancy manipulating with them in their free play. It is important to allow plenty of free time to provide this opportunity.
I made PDL's Number Building Staircases to provide a playful platform to explore staircases in more detail. While Cuisenaire Rods in themselves are fun to play with, these platforms provide opportunity for students to explore staircases under specific constraints. I can encourage students to explore odd staircases or even staircases without specifying that we are looking at odd or even numbers. This enables the student to discover the ideas behind odd and even numbers without the jargon. I can also compare staircases more easily using certain play mats.
With each staircase activity, students will develop a deeper sense of how numbers relate to one another and that understanding will gain fluency and fluidity over time. Students will be able to take this understanding and apply it to more complicated notations down the road. Such a strong foundation will carry them far and children can begin playing with staircases in preschool gaining a sense for numbers without needing to even know number names.
If you are interested in play mats for Cuisenaire rods, you can check out these play mats and more at my TPT store. Many play mats also include task cards to give you more ideas on discovering and exploring numbers thru Cuisenaire Rods.